Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional distributions and cross-feature dependencies. Recent work explores generative approaches using diffusion or flow-based models, extending to time series imputation and forecasting. However, scalability remains a challenge. This work proposes a novel method combining recurrent neural networks' efficiency with diffusion models' probabilistic modeling, based on stochastic interpolants and conditional generation with control features, offering insights for future developments in this dynamic field.